Electrical apparatus for solving right triangles



Jan. 6, 1953 R. H. RINES 7 ELECTRICAL APPARATUS FOR SOLVING RIGHT TRIANGLES Filed Sept. 4, 1944 2 SI'IEE'I'S-SHEET l T mum/Z431: 2 five/baa Elma 24 [OM24 a, I'd UM Jbyea alg -L 560 m 26 R. H. RINES 2,624,874 suzcrmcm. APPARATUS FOR sowmc' RIGHT TRIANGLES Jan. 6, 1953 2 SllEETS-SXE'ET 2 Filed Sept. 4, 1944 Ja -v Patented Jan. 6, 1953 OFFICE acres-14 ELECTRICAL APPARATUS FOR SOLVIN RIGHT TRIANGLES Robert Harvey Rines, Brookllne, Mass.

Application September 4, 1944, Serial No. 552,705

6 Claims. (Cl. 843-11) The present invention relates to electric systems, and more particularly to systems designed electrically to solve trigonometric problems.

It is frequently desirable, given the rangeand elevation of an aircraft, to determine its height and ground range. Many methods have been proposed for solving this problem, all of which are disadvantageous in one particular or another.

An object of the present invention, therefore, is, given an acute angle and the hypotenuse of a right triangle, electrically to determine the legs of the triangle.

Another object is to provide a novel system of electrically solving right triangles.

A further object is to provide a novel electrical height computer and ground-range computer.

Another object is to present the results of'the computations on a cathode-ray-tube indicator.

Other and further objects will be explained hereinafter and will be particularly pointed out in the appended claims.

The invention will now be more fully explained in connection with the accompanying drawings, in which Fig. l is a diagrammatic view of circuits and apparatus illustrating a preferred embodiment of the invention designed for determining the height and the ground range of an airplane; Figs. 2, 3 and 4 are views illustrating various wave-forms associated with the apparatus, Fig. 2 illustrating transmitted radio-frequency pulses, Fig. 3 the output of the radio receiver, and Fig. 4 the output of the video stages; Fig. 5 is a detail view of the face of the cathode-ray-tube indicator shown in Fig. 1; Fig. 6 represents a wave form for triggering the sweep circuit; and Fig. 7 is a diagrammatic view ofa preferred self-pulsing radio-transmitter.

Let it be assumed that an airplane i is positioned at A, at a distance R from a point of observation, or the detecting station, 0, and that its elevation is the angle a. The slant range R, constituting the hypotenuse, and the acuate angle a of the right triangle, may be observed, for example, by means of any well-known sounder radio-location equipment, based on the pulse principle. It is desired 'to learn the height H of the airplane and its ground range G, the two legs of the right triangle. This information may, of course, be readily obtained by means of trigonometric tables, or a slide rule, or by mechanical cams and other completely mechanical devices. There are advantages, however, in being able to read these values of! accurately and directly on electrical equipment. There are particular ad- I 2 vantages in being able to use a simple cathoderay-tube indicator to do so.

This result may be attained, according to the present invention, as illustrated in Fig. l, with the aid of a radio-location detector. The detector may comprise any well-known ultra-high-radiofrequency pulse transmitter I, connected by conductors ,to energize a dipole antenna 3 at the focus of a parabolic reflector l. The pulsed radio energy may be, say, 50 centimeters wave-length.

A parasitic reflector 5 may be employed :to m- .flect the radiation from the dipole 3 back on to the parabolic reflector I, whi ch will then direct the energy out towards the airplane object 8. Upon hitting the object 8, the radio pulses become scattered'and reflected back to the parabolic reflector l and to the dipole 3, and are received in the receiver 8. The receiver 9 may also directly pick up the strong transmitted pulses from the transmitter l; in the period of quiescence of the transmitter I, it also receives th echo from the airplane object 8.

The output of the radio-receiver 9 is detected and amplified as direct-current pulses in the detector and video stages I I. Suitable apparatus for performing this function may be found on page 749 of the Radio Engineering" by F. E. Terman, 1937 edition. This video output is fed between the control grid I 3 and the cathode I5 of a special cathode-ray-tube indicator ll. Normally, the electrode I3 is biased negatively with respect to the cathode 15 by, say, a battery 2|, to prevent the electron stream from reaching the oscilloscope face 23 of the cathode-ray tube H. A B-battery l9 constitutes a source of supply between the cathode IS and the anode 25.

When the brightening pulses from the video stages H, however, arrive between the grid 13 and the cathode l5, electrons emitted from the cathode Ii are permitted to be accelerated, in the form of a stream, past the control grid II and the anode 25 of the tube I 1, between the two sets of horizontally and vertically disposed deflection plates 21, 28 and 3|, 33, respectively, and, also, through horizontally and vertically disposed deflection coils l5 and 31, respectively, to impinge finally on the fluoresecent oscilloscope face 23. The plates 29 and 33 are shown grounded.

At the instant that the pulse transmitter l energizes the antenna 3, it also, by way of conductors I6, sends a triggering pulse to a sweep circuit 41 of any conventional, linear or neariinear type such, for example, as is illustrated on page 740 of the said Radio Engineering," by F. E. Terman. This produces a linear or nearr g a 3 linear horizontal-sweep time base between the horizontal-deflection plates 21 and -28, for deflecting the electron stream horizontally. Since the control electrode [3 is biased negatively with respect to the cathode it, however, this sweep, although the sweep voltage is in effect, will not be observable on the oscilloscope face 23. At such times as a pulse is received by the receiver 0, however, and is applied tolift' the-bias ol=l-the grid ll, by way of the detector and the video stages II, a spot 2| does appear on the oscilloscope face 23, at a horizontalrposition corresponding to the value of the sweep voltage between the deflector plates 21 and 2! at that time. If it may be assumed, therefore, for the time being,- that the sweep voltage starts a sweep at the center of the oscilloscope face 23 at the instant that a radio-frequency pulse is emitted towards the object I, then, at the time that an echo pulse is received from the object 8 by the receiver I, the spot 20 of electrons wlll appear on the omilloscope face 23.

The echoes are indicated as a brief series of oscillations at 22 between similarly indicated received pulses 2t corresponding to similar oscillatory transmitted pulses 2|. After rectification, and preferably also amplication, in the detector and video amplifier stages H, the received pulses appearasshownatil andtheecho asshown at ll,- which serve'as brightening pulses for the cathode-ray-tube. The spot 20 will appear at a point horizontally displaced from the center of the oscilloscope face II by a distance proportional to the slant range R. of the object from the antenna 3. The effective length of the time base is thus rendered proportional to the slant range R. The displacement of the spot 2. of

electrons from the center of the oscilloscope face 28 willthus be a measure of the slant range R of the continuously tracked object 1 from the detecting station 0. A grounded battery 39 pro-' duces a voltage acrom a resistor 4| to provide a vertical positioning control of the electron spot by a direct-current potential between the deflector plates ti and 33.

The parts are so adjusted as to-bring the initial point of-irnpingement'of the electron stream on the oscilloscope facei. not at the center of the oscilloscope face 23, as before temporarily assumed, but oil-center, as shown in Fig.5 The major portion of the oscilloscope face 28 is thus made available for display purposes A handwheel 2 may be employed to rotate a gear I by means of a shaft 4. to elevate or depress the radio-location detector comprising the parabolic reflector I. The gear I is shown meshing with a partly geared section II that is rigidly flxed to the parabolic reflector I. The gearing II is such that the reflector I and the antenna 3 may be swlmg from the horizontal only to the zenith. The gear I may be flxed to a shaft it which. in turn, may rotate a magnetic-fieldproducing element II. The parts may be so arranged that, when the parabolic reflector I is pointing horizontally, the magnetlc-fleld-producing element i2 is also adjusted in a horizontal position. As the parabolic reflector is elevated to an angle 0., therefore} the magnetic-fleld-producing element It also rotates through an angle a. p

The magnetic-fleld-producing element 12 may constitute the rotor of a self-synchronous motor having a vertically positioned stator coil I and a horizontally positioned stator coil ll. Unlike many prior-art systems in which sweep-circuit 4 V voltages are applied to the time-base-positioning rotor, thereby varying the value of the magnetic field thereof at successive intervals of time in accordance with the sweep-circuit voltages, the present invention contemplates a rotor magnetic field unaflfected by the sweep-circuit voltages, being thus produced at successive intervals of time in substantially the same or constant manner without regard to the instantaneous values of the sweep-circuit voltages. Therotor i2 is illustrated in Fig. 1 in the preferred simple form of a permanent magnet. Voltages will be induced in the coils I4 and It by the fleld of the magnet II as it is moved. As the magnet assumes an angle a. to the horizontal, the voltage in the coil H is proportional to sin a, and the voltage in the coil IE to cos a. The extremities of the coil II are connected to the corresponding ends of a deflection coil 35 associated with the cathode-ray-tube I1, and the coil II is similarly connected to a deflection coil 3! of the tube H. The deflection coils 35 and 31 will thus become energized in such a way that their flelds will be identical with the fields of the respective coils l4 and ii; the fleld in coil 35 will be proportional to sin a, and the fleld in coil 11 to cos a.

Let it be assumed that the bias battery ii is reduced, so that a sweep may be observed on the oscilloscope face 23. The time base will then position itself at an angle a from the horizontal under the action of the voltages in the coils 35 and 31. If, for example, the parabolic reflector is pointing in the horizontal direction, 4:0, the magnet I! will induce a voltage in coil 16 only, and hence'in coil 31 only. This in conjunction with an acUustment of the battery 39, will, say, cause the sweep to appear horizontal. If the parabolic reflector is elevated 90', then the coil it will be solely energized, and hence the coil 35 will alone act on the time base as if it were another magnet or rotor, to cause it to appear vertically on the oscilloscope face. 7

For any angle of elevation or depression of the parabolic reflector 1, therefore, the time base will" assume a corresponding angular orientation with respect to the horizontal on the oscilloscope face 23. Since the positioning voltage is independent of and unaffected by the sweep-circuit voltage, as before stated, variations in the accuracy of the latter cannot affect the former and the an ular orientation of the time base will be always correct.

Since, as before explained, a brightening pulse I is applied to the grid ii of the cathode-ray-tube I1 Etthemoment when the echo is received from the object 8, the time base will brighten at such a point. Further, the distance from the start of the time base on the oscilloscope face to this bright spot is a measure of the slant range 25'. of the object 8, indicating a range corresponding to a pulse traveling from the station 0, a distance R to the object 8 and back a distance R to the station again. And the time base is elevated at an angle a corresponding to the elevation of the parabolic reflector 1, or of the object I from the point of observation 0. Since this time base corresponds to the hypotenuse of the right triangle, or the slant range 2R, the abscissa coordinate on the scope face of the brightened spot 20 on the time base is a measure of the ground range of the object 8 (proportional to R cos a). and the ordinate coordinate is a measure of the height of the object (proportional to R sin a). An image of the right triangle, with its slant range 2R, its ground range 20: and its height 28.

will thus be electrically reproduced on the oscilloscope lace 23. g

A calibrated scale, which may be similar to that shown in Fig. 5, may be painted on the oscilloscope face. The horizontal and vertical units are double those corresponding to the slant range R in order to facilitate reading correctly the ground range (3 and the height H of any target appearing thereon. Radial calibration indicated by circles may also be employed to facilitate reading the slant range R. The outside boundary curve of the scale may also be circular. The transmitted pulse, because of delay in the system, appears as a bright spot 32 at the origin of coordinates, corresponding to the received, amplified and detected pulses 28. The echo 20 from the object will obviously be at a. distance 2R from the transmitted pulse spot 32 at the origin of coordinates.

If'the bias voltage of the battery 2| should be made so great that the time base shall not normally appear on the oscilloscope face 23, then only the spot 23 of electrons corresponding to the object 3 will show on the oscilloscope face 23. The ground and altitude coordinates and the slant range of the object 3 may be readily observed from the spot 23 visible on the oscilloscope face 23.

Any desired radio-frequency pulse transmitter may be employed for energizing the antenna 3, a preferred type being illustrated in Fig. '1. Two transmitting triodes 33 and 40 are connected in push-pull with their cathodes 42 and 44 connected together through a grounded tuned radiofrequency circuit 48. This tuned circuit may assums any desired form, such as a lecher line or a tuned cavity (not shown). The anodes 43 and ill of the tubes 33 and 43 are shown connected together through a tuned circuit com rising a condenser 52 and a coil 54. The control electrodes i6 and SI of the tubes 33 and 44 are connected together and through a condenser 80 to a ground 62. also through a resistor 34 to the grounded plate supply 66. A radio-frequency cho e coil 31 is connected from the plate coil 54 to the plate supply 66 for the purpose of keeping radio freouency out of the supply.

In operation. some disturbance starts the tubes oscillating. The grids 56 and I3 draw electrons from their respective cathodes 42 and 44 to charge the condenser 80 negatively, thereby to stop conduction through the tubes, whereupon the oscillations cease. The condenser 80 thereupon discharges throu h the res stor 84 and the plate battery 66. When sufilcient charge has lea ed oil the condenser 60, the oscillations recommence. The oscillating pulses 26 then produced in the coil 54 are picked up by a coil 33 for transmission by way of the conductors 34 to the dipole 3. To this end, one of the conductors 34 is connected to one terminal of the coil 63 and the other conductor 34 is connected to the other terminal.

A grounded center-tap 10 is connected to one of the conductors 36 and a rectifier 12 is connected through a couplin condenser 14 by a conductor 76 to the said other terminal of the pickup coil 63 and to the said other conductor 34.

The radio energy picked up by the coil 68, therelore, travels not only by way of the conductors 34 to the antenna 3, appearing as transmitted pulses 26, but also by way of the conductor 18 to the condenser 14 and the rectifier l2 and through a radio-frequency choke 13, to appear as direct-current pulses 82 across the resistor 30.

geometrically s Fig. 5. 20

The terminals of the resistor 80 are connected to the conductor 38. The pulse 32 will obviously take place at the same time as the pulse 28.

- The sweep circuit 41 is triggered, therefore, by way of the conductors 38 simultaneously with the pulse energization of the antenna 3. As described in the Terman volume previously mentioned, the pulses 32 may cause the sweep tube (not shown) of the sweep circuit 47 to discharge the sweep condenser (not shown), and the period of quiescence between the pulses 82 will allow the swee condenser to charge, producing a near-linear sweep voltage between the deflector plates 21 and 29.

Because of'the. fact that the sweep starts, then. at the completion of the transmitted pulse 26, it might be inferred that the transmitted pulse spot 32 could not appear on the time base as shown in Since these pulses 26 are not strictly sharp, however, some of the pulse does appear The operability of the device, however, is uneffected by the appearance or non-appearance or this pulse on the screen,

Further modifications will occur to persons skilled in the art, and all such are considered to fall within the spirit and scope of the invention.

as defined in the appended claims.

What is claimed is:

1. An electric system for finding the legs of a right triangle, given the hypotenuse and an acute angle, the said system having, in combination, a cathode-ray tube having a screen provided with a base line having an origin and a line disposed at right angles to the base line, the cathode-ray tube having means for producing an electron stream for impinging on the screen, means for causing the electron stream to impinge normally on the origin and two sets of deflecting means for respectively deflecting the electron stream in two directions at right angles to each other, means connected with the deflecting means for-deflecting the electron stream to trace on the screen a hypotenuse line extendin from the origin along the base line, means comprising a rotor of substantially constant magnetic field angularly adjustable to the said acute angle and a stator, and means connected to the deflecting means and controlled in accordance with the field produced in the stator by the angular movement of the rotor for positioning the hypotenuse line at an acute angle to the base line equal to the acute angle with the length of the hypotenuse line proportional to the length of the hypotenuse, the base line and the line at right angles to the base line being calibrated in units proportional to the units of the hypotenuse line,

2. An electric system for finding the ground range and the height of an elevated distant object having, in combination, a detector angularly adjustable vertically to an angle corresponding to the angle of elevation of the object in order that it may receive a signal from the object, a selfsynchronous motor having a rotor of substantially constant magnetic field and a stator, means controlled in accordance with the angular adjustment of the detector for varying the field of the stator in accordance with the position of the rotor, a cathode-ray tube having a screen provided with a reference line and a reference point, the cathode-ray tube havin means for producing an electron stream for impinging on the screen, and meanscontrolled in accordance with the received signal for causing the electron stream to produce on the screen a time base extending from the reference point of length proportional to the slant rangeoi the object and controlled in accordance with a field corresponding to the field produced in the stator by the movement of therotor to positlon the time base at an angle to the reference line corresponding to the instantaneous angular adjustment of the detector.

3. An electric system for finding the ground range and the height 01 an elevated distant ob- Ject having, in combination, a detector anguiarly adjustable vertically to an angle corresponding to the single of elevation of the object in order that it may receive a signal from the object,- a

sell-synchronous motor having a rotor of substantially constant magnetic field and a stator,

means controlled in accordance with the angular adjustment the detector for varying the field oi the stator in accordance with the position or therotor, a cathode-ray tube having a screen provided with a base line having an origin and a line disposed at right angles to the base line, the cathode-ray tube having means for producing an electron stream for impi ng on the screen and means for causing the electron stream to impinge normally on the origin, the cathoderay tube having also means for deflecting the electron stream to cause the electron stream to trace on the screen a time base extending from the origin. means connected to the detector for causing the effective length of the time base to be made proportional to the slant range or the object, and means for energizing the deflecting means with a field corresponding to the field produced in the stator by the movement oi! the rotor to position the time base at an angle with the base line corresponding to the instantaneous angular adjustment of the detector, the base line and the line at right angles to the base line being calibrated in units proportional to the units of the time base.

4. An electric system for finding the ground range and the height of an elevated distant object having, in combination, a detector angularly adjustable vertically to, but not beyond, the zenith to an angle corresponding to the angle of elevation of the object in order that it may receive a signal from the object, a self-synchronous motor having a rotor of substantially constant magnetic field and a stator, means controlled in accordance with the angular adjustment of the detector for varying the field oi the stator in accordance with the position of the rotor, a cathode-ray tube having a screen provided with a base line having an origin, means for producing an electron stream impinging on the screen and mean for causing the electron stream to impinge normally on the origin, the cathode-ray tube having also means for deflecting the electron stream to trace on the screen a time base extending from the origin, means connected to the detector for causing the eflective length of the time base to be made proportional to the slant range of the object, means for energizing the deflecting means with a field corresponding to the field produced in the stator by the ovement of the rotor to position the time base at an angle with the base line corresponding to the instantaneous angular adjustment of the detector, and means connected to the deflecting means for cit-setting the origin of the time base in order that the time base shall be disposed on the major portion of the screen corresponding to all angles of elevation up to the zenith.

5. An electric system for finding the ground range and the height of an elevated distant ob- 8 Ject having, in combination, a radio transmitter for transmitting pulses of radio waves to the object, a radio receiver, the transmitter and the receiver having common directive antenna means for directing and receiving, respectively, radio waves and the same transmitted radio waves aiter scattering or reflection from the object, means for converting part of the energy of the transmitted radio waves into triggering pulses corresponding to the transmitted radio pulses, the antenna means being angularly adjustable to an angle corresponding to the angle of elevation of the object in order that it may receive the scattered or reflected radio waves, a self-synchronous motor having a rotor oi. substantially constant magnetic field and a stator, means controlled in accordance with the angular adiustment of the antenna means for varying the field of the stator in accordance with the position of the rotor, means triggered by the triggering pulses for producing a, time base, means responsive to the scattered or reflected radio waves received by the receiver for causing the eflective length 01' the time base to be made proportional to the slant range of the object, and means controlled in accordance with the field produced in the stator by the movement of the rotor to position the time base at an angle corresponding to the instantaneous an ular adjustment of the detector.

6. An electric system for finding the ground range and the height of an elevated distant object having, in combination, a radio transmitter for transmitting pulses of radio waves to the object, a radio receiver. the transmitter and the receiver having common directive antenna means for directing and receiving, respectively, radio waves and the same radio waves after scattering or reflection from the object, means for converting part of the energy of the transmitted radio waves into triggering pulses corresponding to the transmitted radio pulses, the antenna means being angularly adjustable to an angle corresponding to the angle of elevation oi the object in order that it may receive the scattered or reflected radio waves, a self-synchronous motor having a rotor of substantially constant magnetic field and a stator, means controlled in accordance with the angular adjustment of the antenna means for varying the field of the stator in accordance with the position or the rotor, a cathode-ray tube having a screen provided with a base line having an origin, means for producing an electron stream impinging on the screen and means for causing the electron stream to impinge normally on the origin, means triggered by the said triggering pulses and connected to the deflecting means for deflecting the electron stream to trace on the screen a time base extending from the origin, means responsive to the received scattered or refiected radio waves received by the receiver for causing the efi'ective length 01 the time base to be made proportional to the slant range 01' the object, and means for energizing the deflecting means with a field corresponding to the field prO- duced in the stator by the movement or the rotor to position the time base at an angle to the base line corresponding to the instantaneous angular adjustment or the detector.

ROBERT HARVEY RINIS.

(References on following page) Number REFERENCES CITED 2,426,189 The following references are of record in the 3 1 file of this patent: 2,337,286 UNITED STATES PATENTS 5 19'397 Number Name Date 2,151,917 Hyland Mar. 28, 1939 Number 2,400,791 Tolson May 21, 1946 520,778 2,405,231 Newhouse Aug. 6, 1946 10 543,638 2,409,456 T015011 et a1 Oct. 15, 1946 2,412,631 Rice Dec. 17, 1946 Name Date Espenschled Aug. 26, 1947 Hershberger Nov. 4, 1947 Witt Mar. 9, 1948 Ranger Aug. 22, 1950 FOREIGN PATENTS Country Date Great Britain May 3, 1940 Great Britain Mar. 5, 1942 

